Authors:

James Glazier(Center for Biocomplexity, Department of Physics, Indiana University Bloomington, USA)

The Cellular Potts Model (CPM) is a robust cell level methodology
for simulation of biological tissues and morphogenesis.
Standard diffusion
solvers in the CPM use finite difference methods on the underlying
CPM lattice. These methods have difficulty in simulating local
advection in the ECM due to physiology and morphogenesis. To
circumvent the problem of instabilities we simulate
advection-diffusion within the framework of CPM using off-lattice
finite-difference methods. We define a set of generalised fluid
"cells" or particles which separate advection and diffusion
from the
lattice. Diffusion occurs between neighboring fluid cells by local
averaging rules which approximate the Laplacian. CPM movement
of the
cells by spin flips handles the advection. The extension allows
the CPM
to model viscosity explicitly by including a
relative velocity constraint on the fluid. The extended CPM
correctly
reproduces flow profiles of
viscous fluids in cylindrical tube, during Stokes flow across a
sphere and
in flow in concentric cylindrical shells. We illustrate various
conditions for diffusion including multiple instantaneous sources,
continuous
sources, moving sources and different boundary geometries and
conditions to validate our approximation by comparing with
analytical and established numerical solutions.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2005.MAR.R1.199